Karnataka SSLC Elements of Electrical Engineering IV - JTS (KSEAB) cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R. Units: volt, ampere, ohm, watt.

Series circuit: same current through all elements; R_total = R₁ + R₂ + …; voltage divides in ratio of resistances.

Parallel circuit: same voltage across all branches; 1/R_total = 1/R₁ + 1/R₂ + …; current divides inversely with resistance.

Resistance of a conductor: R = ρL/A; ρ in Ω·m, L in m, A in m². Longer or thinner wire gives higher resistance.

Temperature coefficient: R_t = R₀(1 + αΔt); metals have positive α, carbon and electrolytes negative.

Kirchhoff's laws: KCL - algebraic sum of currents at a node is zero; KVL - algebraic sum of emfs and drops round a loop is zero.

Energy: W = Pt; 1 kWh (one unit) = 3.6 × 10⁶ J. Energy in kWh = watts × hours ÷ 1000.

Cells: emf E, internal resistance r; terminal voltage V = E − Ir on discharge. Series connection raises emf, parallel raises current capacity.

Magnetic flux Φ in weber (Wb); flux density B = Φ/A in tesla (Wb/m²).

Magnetomotive force mmf = NI (ampere-turns); magnetising force H = NI/l in A/m.

Reluctance S = l/(μ₀μ_r A); magnetic Ohm's law: Φ = mmf/S.

Force on a current-carrying conductor: F = BIl sin θ; direction by Fleming's left-hand rule.

Faraday's law: e = −N dΦ/dt; Lenz's law fixes the direction opposing the change producing it.

Self-induced emf e = −L di/dt; energy stored in an inductor W = ½LI².

B–H curve: initial and maximum permeability; saturation limits flux for a given mmf; hysteresis loss ∝ frequency × area of loop.

Series magnetic circuit: total reluctance is the sum of the parts; air gaps dominate because μ_r of air is 1.

RMS = peak/√2 = 0.707 × peak; average of a full sine = 0; form factor 1.11, peak factor 1.414.

Frequency f = 1/T; angular frequency ω = 2πf; a 50 Hz supply has 100 pulses per second in a full-wave rectifier.

Pure R: current in phase with voltage. Pure L: current lags voltage by 90°. Pure C: current leads by 90°.

Reactances: X_L = 2πfL (rises with f); X_C = 1/(2πfC) (falls with f).

Impedance Z = √(R² + (X_L − X_C)²); phase angle tan φ = (X_L − X_C)/R.

Power: P = VI cos φ (watt), Q = VI sin φ (var), S = VI (VA); power factor = cos φ = R/Z.

Series resonance: X_L = X_C, Z = R minimum, current maximum, f_r = 1/(2π√(LC)).

Single-phase power factor improvement uses a parallel capacitor: I_C = P(tan φ₁ − tan φ₂)/V.

Star: V_L = √3 V_ph, I_L = I_ph. Delta: V_L = V_ph, I_L = √3 I_ph.

Three-phase power P = √3 V_L I_L cos φ; for balanced star or delta the same formula applies.

Phase sequence and 120° displacement give constant total power in a balanced three-phase load.

Transformer emf equation: E = 4.44 f N Φ_m; voltage ratio V₂/V₁ = N₂/N₁ = I₁/I₂.

Ideal transformer: input VA equals output VA; core loss is constant, copper loss varies as I².

Losses: hysteresis and eddy-current (core) losses plus I²R (copper) losses; efficiency is maximum when copper loss equals core loss.

Open-circuit test gives core loss; short-circuit test gives full-load copper loss and equivalent impedance.

An autotransformer shares one winding; a current transformer steps current down for measurement and must never be open-circuited on the secondary.

DC generator emf: E_g = ΦZN P/(60A); for a DC motor back emf E_b = V − I_a R_a.

Motor torque T ∝ Φ I_a; speed N ∝ (V − I_a R_a)/Φ, so a shunt motor is nearly constant-speed.

A DC series motor must never be started unloaded; it develops high torque at low speed.

Three-phase induction motor: synchronous speed N_s = 120f/P; slip s = (N_s − N)/N_s; rotor frequency = sf.

Induction motor is self-starting, has no electrical connection to the rotor (squirrel cage), and runs below synchronous speed.

Synchronous motor runs at exactly N_s and can supply leading reactive power (used for power-factor correction).

Single-phase induction motors are not self-starting in principle; capacitor and shaded-pole types create a rotating field.

Alternator frequency f = PN/120; emf per phase E = 4.44 f Φ T k_d k_p.

Indian wiring colours: phase red/yellow/blue, neutral black, earth green (or green-yellow).

Copper has lower resistivity than aluminium, so a smaller copper conductor carries the same current.

Fuse rating rule: fuse current slightly above normal load current but below the cable's current rating.

MCB trips on overload (thermal) and short circuit (magnetic); ELCB/RCCB trips on earth leakage, typically 30 mA for personnel protection.

Earthing limits touch voltage; earth resistance should be low (commonly ≤ 1 Ω for substations, a few ohms for domestic).

Two-way switching uses two two-way switches; the intermediate (three-way) switch is added for three control points.

Wire gauge (SWG) increases as the number decreases; a lower SWG number means a thicker wire.

Conduit, casing-capping and cleat wiring are chosen by location: conduit for concealed and damp areas, cleat for temporary open runs.

Ammeter is connected in series and has very low resistance; voltmeter in parallel with very high resistance.

PMMC instrument: deflecting torque T = NABI, reads average value, used with rectifier for AC.

Moving-iron instrument reads RMS, is robust, and suits both AC and DC.

Induction type energy meter: deflecting torque ∝ power; creep prevented by a brake magnet and shading.

Wattmeter has a current coil (series) and a pressure coil (parallel); reading is VI cos φ.

Meter constant is revolutions per kWh; energy = revolutions ÷ meter constant.

Tariff: two-part tariff = fixed charge + running charge per unit; power factor penalty applies below a set cos φ.

Energy = power × time; a 1000 W load for 2 hours consumes 2 units (kWh).

First aid for electric shock: switch off the supply, use dry insulating material to separate the victim, then start artificial respiration if breathing has stopped.

Never use water on an electrical fire; use CO₂ or dry-powder extinguishers.

Earth-leakage protection of 30 mA is the usual threshold for protection of persons against fatal shock.

Energy conservation: replace incandescent lamps with LED, use electronic chokes, and improve power factor to cut line current.

Illumination: luminous flux in lumen, illuminance in lux (lumen per m²); LED gives more lumen per watt than incandescent.

Load estimation: total connected load in watts ÷ 1000 gives kW; diversity factor reduces the maximum demand used for billing.

A star-delta starter reduces starting current to one-third of the direct-on-line value.

Periodic inspection checks insulation resistance (megger), earth continuity and correct fuse/MCB ratings.